The Malyuzhinets theory for scattering from wedge boundaries: A review

Wave Motion

Volumn 29, Issue 4, 1999, Pages 313-340

  Osipov, A V ^a   Norris, A N ^b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DIFFRACTION; INTEGRAL EQUATIONS; INVERSE PROBLEMS; LAPLACE TRANSFORMS; PROBLEM SOLVING; SCATTERING; THEOREM PROVING;

BESSEL FUNCTIONS; MALYUZHINETS THEORY; NULLIFICATION THEOREM; SOMMERFELD INTEGRALS; WEDGE BOUNDARIES;

WAVEFORM ANALYSIS;

EID: 0032624459     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-2125(98)00042-0     Document Type: Article

References (88)

1. J.J. Bowman, T.B.A. Senior, The Wedge, in: J.J. Bowman, T.B.A. Senior, P.L.E. Uslenghi (Eds.), Electromagnetic and Acoustic Scattering by Simple Shapes, North-Holland, Amsterdam, 1969, pp. 252-283.
2. A.D. Pierce, Acoustics: An Introduction to its Physical Principles and Applications, Acoustical Society of America, Woodbury, NY, 1989.
3. G.I. Petrashen', B.G. Nikolaev, D.P. Kouzov, On the method of series in the theory of diffraction of waves from flat angular regions, Leningrad State University Scientific Reports: Math. Sci. 246 (1958) 5-165 (in Russian).
4. Oberhettinger F. On the diffraction and reflection of waves and pulses by wedges and corners. J. Res. NBS. 61:1958;343-365.
5. Tuzhilin A.A. New representations of diffraction fields in wedge-shaped regions with ideal boundaries. Sov. Phys. Acoust. 9:1963;168-172.
6. Ambaud P., Bergassoli A. The problem of the wedge in acoustics. Acustica. 27:1972;291-298.
7. L.B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves, Prentice Hall, New York, 1978.
8. W.J. Hadden, Jr., A.D. Pierce, Sound diffraction around screens and wedges for arbitrary point source locations, J. Acoust. Soc. Am. 69 (1981) 1266-1276. Erratum: J. Acoust. Soc. Am. 71 (1982) 1290.
9. W.J. Hadden, Jr., A.D. Pierce, Sound diffraction around screens and wedges for arbitrary point source locations, J. Acoust. Soc. Am. 69 (1981) 1266-1276. Erratum: J. Acoust. Soc. Am. 71 (1982) 1290.
10. DeWitt-Morette C., Low S.G., Schulman L.S., Shiekh A.Y. Wedges I. Foundations of Physics. 16:1986;311-349.
11. G.D. Malyuzhinets, Generalisation of the Reflection Method in the Theory of Diffraction of Sinusoidal Waves, Doctoral dissertation, P.N. Lebedev Phys. Inst. Acad. Sci. USSR, 1950 (in Russian).
12. Malyuzhinets G.D. The radiation of sound by the vibrating boundaries of an arbitrary wedge. Part I. Sov. Phys. Acoust. 1:1955;152-174.
13. Malyuzhinets G.D. Radiation of sound from the vibrating faces of an arbitrary wedge Part II. Sov. Phys. Acoust. 1:1955;240-248.
14. Malyuzhinets G.D. Inversion formula for the Sommerfeld integral. Sov. Phys. Dokl. 3:1958;52-56.
15. Malyuzhinets G.D. Relation between the inversion formulas for the Sommerfeld integral and the formulas of Kontorovich-Lebedev. Sov. Phys. Dokl. 3:1958;266-268.
16. Malyuzhinets G.D. Excitation, reflection and emission of surface waves from a wedge with given face impedances. Sov. Phys. Dokl. 3:1958;752-755.
17. G.D. Malyuzhinets, Das Sommerfeldsche Integral und die Lösung von Beugungsaufgaben in Winkelgebieten, Ann. Phys. 6 (1960) 107-112, in German.
18. Williams W.E. Diffraction of an E-polarised plane wave by an imperfectly conducting wedge. Proc. R. Soc. London A. 252:1959;376-393.
19. Senior T.B.A. Diffraction by an imperfectly conducting wedge. Comm. Pure Appl. Math. 12:1959;337-372.
20. A.A. Tuzhilin, Theory of Malyuzhinets' functional equations. I. Homogeneous functional equations, general properties of their solutions, particular cases, Differents. Uravnenija 6 (1970) 692-704 (in Russian).
21. A.A. Tuzhilin, Theory of Malyuzhinets' functional equations. II. The theory of Barnes' infinite products. General solutions of homogeneous Malyuzhinets' functional equations. Various representations of the basis solutions, Differents. Uravnenija 6 (1970) 1048-1063 (in Russian).
22. A.A. Tuzhilin, Theory of Malyuzhinets' functional equations. III. Non-homogeneous functional equations. The general theory, Differents. Uravnenija 7 (1971) 1077-1088 (in Russian).
23. A.A. Tuzhilin, Diffraction of a plane sound wave in an angular region with absolutely hard and slippery faces covered by thin elastic plates, Differents. Uravnenija 9 (1973) 1875-1888 (in Russian).
24. G.D. Malyuzhinets, An accurate solution to a problem of diffraction of a plane wave by a semi-infinite elastic plate, Proc. 4th All-Union Acoustics Conf., vol. 45, Academy of Science, Moscow, USSR, 1958 (in Russian).
25. G.D. Malyuzhinets, A.A. Tuzhilin, Diffraction of a plane sound wave by a thin semi-infinite elastic plate, Zh. Vych. Matem. i Matem. Fiz. 10 (1970) 1210-1227 (in Russian).
26. G.D. Malyuzhinets, Sound diffraction and the surface waves propagating over a semi-infinite elastic plate, Trudy Akust. Inst. 15 (1971) 80-96 (in Russian).
27. M.P. Sakharova, A.F. Filippov, Solution of a nonstationary problem of diffraction by an impedance wedge in tabulated functions, Zh. Vych. Matem. i Mat. Fiziki 7 (1967) 568-579 (in Russian).
28. A.F. Filippov, Investigation of solution of a nonstationary problem of diffraction of a plane wave by an impedance wedge, Zh. Vych. Matem. i Mat. Fiziki 7 (1967) 825-835 (in Russian).
29. Φ (z) , Akust. Inst. Rep., Moscow, 1961.
30. Φ in problems of wave diffraction in wedge-shaped regions Sov. Phys. Acoust. 13:1967;48-54.
31. M.P. Sakharova, On asymptotic expansion of certain functions occurring in the wedge diffraction theory, Izv. Vuzov. Fizika (11) (1970) 141-144 (in Russian).
32. Volakis J.L., Senior T.B.A. Simple expressions for a function occurring in diffraction theory. IEEE Trans. Antennas Propagat. 33:1985;678-680.
33. Hongo K., Nakajima E. Polynomial approximation of Malyuzhinets' function. IEEE Trans. Antennas Propagat. 34:1986;942-947.
34. Herman M.I., Volakis J.L., Senior T.B.A. Analytic expressions for a function occurring in diffraction theory. IEEE Trans. Antennas Propagat. 35:1987;1083-1086.
35. Osipov A.V. Calculation of the Malyuzhinets function in a complex region. Sov. Phys. Acoust. 36:1990;63-66.
36. Aidi M., Lavergnat J. Approximation of the Maliuzhinets function. Journal of Electromagnetic Waves and Applications. 10:1996;1395-1411.
37. Jin-Lin Hu, Shi-Ming Lin, Wen-Bing Wang Calculation of Maliuzhinets function in complex region. IEEE Trans. Antennas Propagat. 44:1996;1195-1196.
38. B.V. Budaev, G.I. Petrashen', On efficient approaches to solving the problem of wave diffraction from wedge-shaped regions, in: Problems of the Dynamic Theory of Seismic Wave Propagation, Steklov Mathematical Institute, Leningrad, vol. 23, 1983, pp. 78-91 (in Russian).
39. Osipov A.V. Diffraction of a plane wave in a corner region with impedance boundary conditions. Sov. Phys. Acoust. 37:1991;381-385.
40. Bowman J.J. High-frequency scattering from an absorbing infinite strip with arbitrary face impedance. Can. J. Phys. 45:1967;2409-2430.
41. Bucci O.M., Franceschetti G. Electromagnetic scattering by a half-plane plane with two face impedances. Radio Sci. 11:1976;49-59.
42. S.N. Karp, F.C. Karal, A new method for the determination of the far-fields with applications to the problem of radiation of a line source at the tip of an absorbing wedge, IEEE Trans. Antennas Propagat. 7 (1959) S91-S102.
43. Williams W.E. Propagation of electromagnetic surface waves along wedge surfaces. Quart. J. Mech. Appl. Math. 13:1960;278-284.
44. Williams W.E. Vertex generated waves outside metallic wedges. Proc. Cambridge Phil. Soc. 57:1961;393-400.
45. R.P. Starovoitova, M.S. Bobrovnikov, Excitation of an impedance wedge by a line magnetic current placed at the vertex, Izv. Vuzov. Fizika (4) (1962) 130-139 (in Russian).
46. M.S. Bobrovnikov, V.V. Fisanov, Diffraction of Waves in Sector Regions, Tomsk State University, Tomsk, Russia, 1988 (in Russian).
47. Pelosi G., Tiberio R., Rojas R.G. Electromagnetic field excited by a line source placed at the edge of an impedance wedge. IEEE Trans. Antennas Propagat. 39:1991;1043-1046.
48. Otero M.F., Rojas R.G. Two-dimensional Green's function for a wedge with impedance faces. IEEE Trans. Antennas Propagat. 45:1997;1799-1809.
49. Osipov A., Hongo K. The Green function of an impedance wedge. Electromagnetics. 18:1998;135-167.
50. Zavadskaya M.P., Starovoitova R.P. Edge waves in G.D. Malyuzhinets' solution for an impedance wedge. Sov. Phys. Acoust. 34:1988;678-680.
51. R.P. Starovoitova, M.S. Bobrovnikov, V.N. Kislicyna, Diffraction of a surface wave by an edge in an impedance plane, Radiotekh. Elektron. 7 (1962) 250-259 (in Russian).
52. M.S. Bobrovnikov, V.N. Ponomareva, V.G. Myshkin, R.P. Starovoitova, Diffraction of a skewly incident surface wave by an edge in an impedance surface, Izv. Vuzov. Fizika 1 (1965) 162-169 (in Russian).
53. Pierce A.D., Hadden W.J. Jr. Plane wave diffraction by a wedge with finite impedance. J. Acoust. Soc. Am. 63:1978;17-27.
54. Griesser T., Balanis C.A. Reflections, diffractions, and surface waves for an interior impedance wedge of arbitrary angle. IEEE Trans. Antennas Propagat. 37:1989;927-935.
55. Osipov A.V. Uniform asymptotic formula for calculating an acoustic field near a face of an impedance wedge. Sov. Phys. Acoust. 36:1990;180-183.
56. Osipov A.V. Asymptotic representation of the sound field in a narrow angular region with impedance boundaries. Sov. Phys. Acoust. 36:1990;287-290.
57. A.V. Osipov, On radar invisibility of an impedance wedge, IEEE AP-S Int. Symposium and URSI North American Radio Science Meeting, Montreal, Quebec, Canada, 13-18 July 1997, URSI Digest, p. 724.
58. James G.L. Uniform diffraction coefficients for an impedance wedge. Electron. Lett. 13:1977;403-404.
59. Tiberio R., Pelosi G., Manara G. A uniform GTD formulation for the diffraction by a wedge with impedance faces. IEEE Trans. Antennas Propagat. 33:1985;867-873.
60. Pelosi G., Maci S., Tiberio R., Michaeli A. Incremental length diffraction coefficients for an impedance wedge. IEEE Trans. Antennas Propagat. 40:1992;1201-1210.
61. M.S. Bobrovnikov, R.P. Starovoitova, Diffraction of cylindrical waves by an impedance wedge, Izv. Vuzov. Fizika (6) (1963) 168-176 (in Russian).
62. Tiberio R., Pelosi G., Manara G., Pathak P.H. High-frequency c scattering from a wedge with impedance faces illuminated by a line source, Part I: Diffraction. IEEE Trans. Antennas Propagat. 37:1989;212-218.
63. V.F. Kravchenko, V.M. Likhachev, A.I. Stashkevich, On one asymptotic method of solution of a boundary-value problem for impedance wedge excitation, Dokl. Akad. Nauk USSR 308 (1989) 329-334 (in Russian).
64. V.M. Likhachev, A.I. Stashkevich, Diffraction of a cylindrical wave in an impedance angular region, Radiotekh. Electron. 35 (1990) 707-717 (in Russian).
65. Manara G., Tiberio R., Pelosi G. High-frequency scattering from a wedge with impedance faces illuminated by a line source, Part II: Surface waves. IEEE Trans. Antennas Propagat. 41:1993;877-883.
66. Lebedev N.N., Skal'skaja I.P. A new method for solving the problems of diffraction of electromagnetic waves by a wedge of finite conductivity. Sov. Phys. Tech. Phys. 4:1962;627-637.
67. B. Budaev, Diffraction by Wedges, Longman Scientific and Technical, UK, 1995.
68. B. Noble, Methods Based on the Wiener-Hopf Technique, Pergamon Press, London, 1958.
69. Karal F.C., Karp S.N. Diffraction of a skew plane electromagnetic wave by an absorbing right angled wedge. Comm. Pure Appl. Math. 11:1958;495-533.
70. Karal F.C., Karp S.N., Kouyoumjian R.G. Scattering of a surface wave by a discontinuity in the surface reactance on a right-angled wedge. Comm. Pure Appl. Math. 14:1961;35-48.
71. Williams W.E. Diffraction by an imperfectly conducting wedge. Proc. Cambr. Phil. Soc. 55:1959;195-209.
72. Williams W.E. A note on the diffraction by a right-angled wedge. Proc. Cambr. Phil. Soc. 61:1965;275-278.
73. T.B.A. Senior, Some problems involving imperfect half plane, in: P.L.E. Uslenghi (Ed.), Electromagnetic Scattering, Academic Press, New York, 1978.
74. T.B.A. Senior, J.L. Volakis, Approximate Boundary Conditions in Electromagnetics, IEE Press, Stevenage, UK, 1995.
75. Norris A.N., Wickham G.R. Acoustic diffraction from the junction of two flat plates. Proc. R. Soc. Lond. A. 451:1995;631-656.
76. Van Lennep A.G.R. The kernel of Sommerfeld's transform as solution to difference equations for a class of diffraction problems. J. Appl. Phys. 45:1974;4401-4405.
77. A.V. Osipov, Malyuzhinets transform and the method of Sommerfeld integral in the theory of diffraction of waves in wedge-shaped domains, in: Problems of Diffraction and Wave Propagation, St. Petersburg State University, St. Petersburg, Russia, vol. 25, 1993, pp. 148-173.
78. A.N. Norris, A.V. Osipov, Far-field analysis of the Malyuzhinets solution for plane and surface waves diffraction by an impedance wedge, Wave Motion (1998), accepted.
79. F.W.J. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974.
80. R. Mittra, S.W. Lee, Analytical Techniques in the Theory of Guided Waves, Macmillan, New York, 1974.
81. A.V. Osipov, General solution for a class of diffraction problems, J. Phys. A: Math. Gen. 27 (1994) L27-L32.
82. Abrahams I.D., Lawrie J.B. Travelling waves on a membrane: reflection and transmission at a corner of arbitrary angle I. Proc. Roy. Soc. Lond. A. 451:1995;657-683.
83. Lawrie J.B., Abrahams I.D. Travelling waves on a membrane: reflection and transmission at a corner of arbitrary angle. II. Proc. Roy. Soc. Lond. A. 452:1996;1649-1677.
84. Osipov A.V. Diffraction by a wedge with higher-order boundary conditions. Radio Sci. 31:1996;1705-1720.
85. Ljalinov M.A. Diffraction of a plane wave by a wedge with thin material coatings. Radio Sci. 31:1996;1721-1730.
86. Osipov A.V., Norris A.N. Acoustic diffraction by a fluid-loaded membrane corner. Proc. Roy. Soc. Lond. A. 453:1997;43-64.
87. Norris A.N., Osipov A.V. Structural and acoustical wave interaction at a wedge-shaped junction of fluid loaded plates. J. Acoust. Soc. Am. 101:1997;867-876.
88. C.C. Constantinou, C. Demetrescu, A.V. Osipov, Diffraction by an impedance wedge at oblique incidence, Proc. 1998 URSI Int. Symp. on Electromagnetic Theory, 25-27 May 1998, Thessaloniki, Greece, pp. 402-404.